Came upon on the flip of the twentieth century, p-adic numbers are usually utilized by mathematicians and physicists. this article is a self-contained presentation of simple p-adic research with a spotlight on analytic subject matters. It bargains many good points infrequently taken care of in introductory p-adic texts reminiscent of topological versions of p-adic areas within Euclidian house, a distinct case of Hazewinkel’s useful equation lemma, and a remedy of analytic parts.

Elliptic stories describes the newest advancements in quantity conception through taking a look at essentially the most intriguing unsolved difficulties in modern mathematics—the Birch and Swinnerton-Dyer Conjecture. during this booklet, Avner Ash and Robert Gross advisor readers throughout the arithmetic they should comprehend this beautiful challenge.

An creative creation to quantity conception, this special approach employs a couple of fictional characters, Ant and Gnam. Ant leads Gnam via numerous theories, and jointly, they positioned the theories into action—applying linear diophantine equations to soccer scoring, utilizing a black-magic equipment to simplify difficulties in modular buildings, and constructing interesting adjustments to the principles of chess.